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<em>v.net.flow</em> computes the maximum flow and minimum cut
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between two sets of nodes.
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The two sets of nodes are called <em>sources</em> and <em>sink</em>
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and <em>v.net.flow</em> finds the maximimum flow from the former to
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the latter ones. Edge capacities can be specified by <b>arc_column</b>
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for forward direction and <b>arc_backward_column</b> for backward direction. If
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the latter parameter is ommited then the same capacity is used in
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either direction. The sets are given by the respective <b>cats</b>,
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<b>layer</b> and <b>where</b> parameters. Maximum flow corresponds
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to the maximum amount of water possibly flowing through the network
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preserving the capacity constraints and minimum cut to the set of edges
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of minimum total capacity completely separating sources from sinks.
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The cut produced by this module corresponds to the first fully
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saturated edges from sources to sinks. An attribute table containing
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the flow information is linked to the <b>output</b> map. The table
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consists of two columns: <em>cat</em> and <em>flow</em> and stores
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the flow along each line. Negative flow means that "water" is
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flowing in the backward direction. <b>Cut</b> map contains the edges
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A famous <a href="http://en.wikipedia.org/wiki/Max-flow_min-cut_theorem">result</a>
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says that the total amount of water flowing is equal to the minimum
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Find maximum flow from factories to stores using SPEED for the capacities.
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<div class="code"><pre>
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v.net.flow input=roads output=roads_flow cut=roads_cut arc_column=SPEED \
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source_where="type=factory" sink_where="type=store"
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If all the capacties are one then the minimum cut corresponds to the
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minimum number of edges separating sources from sinks.
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<div class="code"><pre>
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v.net.flow input=network output=flow cut=cut arc_column=ones \
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source_cats=1-10 sink_cats=100-100
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<a href="v.net.html">v.net</a>,
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<a href="v.net.connectivity.html">v.net.connectivity</a>
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Daniel Bundala, Google Summer of Code 2009, Student<br>
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Wolf Bergenheim, Mentor
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<p><i>Last changed: $Date: 2014-12-24 15:44:33 +0100 (Wed, 24 Dec 2014) $</i>